FIG. 1 depicts a schematic diagram of wireless telecommunications system 100 which provides wireless telecommunications service to wireless terminal 101 within a region. The heart of the telecommunications system is wireless switching center 111, which might also be known as a mobile switching center (“MSC”) or a mobile telephone switching office (“MTSO”).
Typically, wireless switching center 111 is connected to a plurality of base stations (e.g., base stations 102-1, 102-2, and 102-3), which are dispersed throughout the geographic area serviced by the system. As depicted in FIG. 1, base station 102-2 serves wireless terminal 101.
As is well known to those skilled in the art, wireless switching center 111 is responsible for, among other things, establishing and maintaining calls between wireless terminals and between a wireless terminal and a wireline terminal (which is connected to the system via the local and/or long-distance telephone networks).
A base station and a wireless terminal served by the based station communicate via radio-frequency (which is also called “RF”) signals. As is well known to those skilled in the art, a signal's strength attenuates as it travels along the path from the transmitter to a receiver. The factors that cause the loss in signal strength include (i) the distance of the signal's path, and (ii) presence of radio-frequency obstacles (e.g., hills, trees, and buildings, etc.) in the signal's path and (iii) off-path scatterers.” The amount of loss or attenuation of a signal's strength along its path is known as “path loss.”
Because the distance from a transmitter to most locations is different, and in most places the quantity and quality of the radio-frequency obstacles is different in every direction and at different distances from the transmitter, the path loss from the transmitter to most locations varies. Because the path loss from the transmitted to most locations varies, the strength of a transmitted signal at most locations varies as well. For this reason, the path loss and the strength of a received signal are related to each other. In other words, as the path loss increases, the received signal's strength decreases, and as the path loss decreases, the received signal strength increases.
As is well-known to those skilled in the art, the location of a wireless terminal can be estimated by comparing the strength of a received signal at the wireless terminal against a map that correlates signal strength to location. A map that correlates received signal strength to location is known as a “path-loss map.”
There are two ways to generate a path-loss map. In accordance with the first way, a test of the signal's strength is empirically measured at every location on the map. Although this provides an accurate map, it is usually prohibitively expensive because there are often a large number of locations at which measurements need to be taken.
In accordance with a second way, a test of the signal's strength is empirically measured at some locations and then the signal strength at the other locations is predicted using interpolation and extrapolation. When the techniques for interpolation and extrapolation are well-chosen, this can provide an economically-reasonable and accurate path-loss map.
The production and updating of path-loss maps has historically been difficult and expensive, and path-loss maps are often inaccurate at specific locations. In fact, some industrial path-loss maps are off as much as 15 to 20 dB at specific locations, which effectively eliminates their usefulness in estimating the location of a wireless terminal based on signal-strength measurements.
Although linear interpolation and extrapolation can be used, more sophisticated mathematical techniques yield more accurate path-loss maps. In the industry, these mathematical techniques are called “path-loss” or “radio-frequency propagation” models. In general, a path-loss model comprises one or more parameters that are fitted into the empirical signal-strength measurements.
FIG. 2 depicts a flowchart of the salient tasks performed in calibrating an path-loss model for a particular geographic area, in the prior art.
At task 210, a path-loss model is selected.
At task 220, a signal-strength measurement is taken at each of a plurality of locations within the geographic area.
At task 230, the values for the parameters in the path-loss model are fitted based on the measurements received at task 220.
At task 240, the path-loss model outputs the predicted signal-strength at each location to form the path-loss map.
The earliest techniques for predicting path loss for wireless networks, which still persist in current planning tools, were simple statistical models based on transmitter-receiver distance. The Hata model and the COST-231 model (an extension of the Hata model) are two popular examples. It is not unusual, however, for these models to produce errors of predicted versus empirical measurements of 10 to 20 dB.
Transmitter-receiver distance models, such as the Hata and COST-231 models, are typically based on the following equations:
                                          RSSI            dBm                    =                                    P                              T                ,                dBm                                      +                          G              T                        +                          G              R                        -                          PL              ⁢                                                          ⁢                              (                                  d                  ref                                )                                      -            PathLoss                          ⁢                                  ⁢        and                            (                  Eq          .                                          ⁢          1                )                                          PL          ⁢                                          ⁢                      (                          d              ref                        )                          =                  20          ⁢                                    log              10                        ⁡                          (                                                4                  ⁢                  π                  ⁢                                                                          ⁢                                      d                    ref                                                  λ                            )                                                          (                  Eq          .                                          ⁢          2                )            wherein:
RSSIdBm=Received power (Received Signal Strength Indication);
PT,dBm=Transmitted power (power into the transmitter antenna);
GT=Gain, in dB, of the transmitter antenna;
GR=Gain, in dB, of the receiver antenna;
dref=reference distance (usually 10 m in this work);
λ=freespace wavelength of radiation;
PL(dref)=reference path loss; and
PathLoss=Path loss (in dB) with respect to dref meter, freespace loss.
The PathLoss term depends on receiver location within the propagation environment and contains all of the random variability. The other terms represent effects in the amplifier chain that, once the carrier frequency is known, are constant.
Equation 1 can alternatively be expressed in terms of effective isotropic radiated power (EIRP), which is the sum of the power into the transmitted antenna (PT,dBm) and the transmitter antenna gain (GT):RSSIdBm=EIRPdBm+GR−PL(dref)−PathLoss  (Eq. 3)Equation 3 is often more useful in practice than Equation 1 because many cellular carriers report EIRP, but do not report one or both of the input transmitter power and the antenna gain.
Another technique for characterizing path loss as a function of transmitter-receiver (TR) separation distance uses path loss exponents. In accordance with this technique, the average dB path loss with respect to 1 m free space is assumed to increase linearly as a function of the logarithm of the distance between the transmitter and the receiver. The slope of this increase is characterized by the path loss exponent, n, in Equation 4:
                    PathLoss        =                  10          ⁢          n          ⁢                                          ⁢                                    log              10                        (                          ⅆ                              ⅆ                ref                                      )                                              (                  Eq          .                                          ⁢          4                )            where d is the distance between the transmitter and the receiver in meters and dref is 1 meter, which is a common reference distance. When radios are operating in free space, the path loss exponent is n=2. When radios are operating near the ground, the path loss exponent is almost always greater than 2.
When a number of path-loss measurements (also known as attenuation measurements) have been taken in an environment, well-known regression techniques (e.g., the minimum mean-squared error regression technique, etc.) can be applied to the measurements to calculate the path loss exponent. When there are N measured locations and PLi denotes the ith path-loss measurement at a distance between the transmitter and the receiver of di, the value for n is given by Equation 5.
                    n        =                                            ∑                              i                =                1                            N                        ⁢                                          PL                i                            ⁢                                                          ⁢                                                log                  10                                (                                                      d                    i                                                        1                    ⁢                    m                                                  )                                                          10            ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                                                [                                                            log                      10                                        (                                                                  d                        i                                                                    1                        ⁢                        m                                                              )                                    ]                                2                                                                        (                  Eq          .                                          ⁢          5                )            An estimate of the standard deviation, σ, for the measured versus predicted path loss based on this data is given by:
                              σ          2                =                              1            N                    ⁢                                    ∑                              i                =                1                            N                        ⁢                                          [                                                      PL                    i                                    -                                      10                    ⁢                    n                    ⁢                                                                                  ⁢                                                                  log                        10                                            ⁡                                              (                                                                              d                            i                                                                                1                            ⁢                            m                                                                          )                                                                                            ]                            2                                                          (                  Eq          .                                          ⁢          6                )            
In general, the path loss experienced by a wireless receiver in the field will be random. Equations 5 and 6 estimate the log-normal statistics of large scale path loss. The log-normal distribution provides a convenient, “best-fit” description for large-scale path loss. For given propagation conditions, such as fixed transmitter-receiver separation distance, a histogram of dB path-loss measurements will assume a Gaussian shape characterized by a mean or average dB value μ, and a standard deviation σ. The value σ represents an approximate two-thirds confidence interval about the dB mean that is predicted by the path loss exponent. The value μ is the path loss calculated from the path loss exponent model. The path loss exponent n that minimizes the standard deviation is useful for gaining quick insight into the general propagation; however, this technique often leads to large, unacceptable standard deviations for prediction at specific locations.
In the 1990s there was a big push in the research community to develop ray tracing techniques for propagation prediction, particularly because the industry was anticipating the proliferation of wireless base stations and prior statistical models, as described above, were ill-suited for the proliferation of wireless base stations. Ray-tracing uses geometrical optics to trace the likely paths of radio waves that reflect and diffract through a digital representation of a cityscape with terrain features. This deterministic approach appealed to many engineers, who expected substantial improvements in model accuracy.
Practitioners of ray-tracing found, however, that while the technique afforded a little more accuracy than prior approaches, it suffered from huge computational costs. Moreover, ray tracing is not a very convenient or scalable technology: engineers often had to spend inordinate amounts of time formatting the maps and data required as inputs to a ray-tracing software engine. In response to these drawbacks, some compromise techniques were developed that employed a balance of additional site data without the complexity and inconvenience of ray-tracing. This class of propagation models, initially developed for indoor usage, was based on basic information such as building blueprints and typically resulted in standard deviation errors of 5-10 dB.
Some path-loss models that use site-specific information can, with a little creativity, be linearized and cast into a matrix format. The linear matrix format is particularly useful because it lends itself to computer evaluation and it can be easily tuned against a set of measurements. As a result, the propagation models become more accurate as more measurements are accumulated.
Matrix-based propagation models have been used in conjunction with computer-generated floor plans to model partition-dependent attenuation factors. These models employ a path loss exponent of n with additional path loss based on the type and number of objects (e.g., interior walls, etc.) between the transmitter and receiver locations. For outdoor-to-indoor propagation environments, these attenuating objects might also include trees, wooded patches, building exteriors, etc. The path loss at any given point is described by Equation 7:
                    PathLoss        =                              10            ⁢            n            ⁢                                                  ⁢                                          log                10                            (                              ⅆ                                  ⅆ                  ref                                            )                                +                      a            ×                          x              a                                +                      b            ×                          x              b                                +          ⋯                                    (                  Eq          .                                          ⁢          7                )            wherein a, b, etc. are integers representing the number of radio-frequency obstacles of each type between the receiver and transmitter, and xa, xb, etc. are their respective attenuation values in dB.
For measured data at a known site, the unknowns in Equation 7 are the individual attenuation factors xa, xb, etc. By tuning these model parameters against known measurements, it is possible to extrapolate a more accurate prediction into unmeasured parts of the propagation environment.
One method of calculating attenuation factors xa, xb, etc. is to minimize the mean squared error of measured versus predicted data in dB. If pi is assigned the path loss measured at the ith location, then N measurements will result in the following system of equations:p1=10n log10(d1)+a1·xa+b1·xb+p2=10n log10(d2)+a2·xa+b2·xb+pN=10n log10(dN)+aN·xa+bN·xb+  (Eq. 8)As is well-known to those skilled in the art, these N equations can be more elegantly written in matrix notation as:
                                          p            →                    =                      A            ⁢                                                  ⁢                          x              →                                      ⁢                                  ⁢        where                            (                  Eq          .                                          ⁢          9                )                                          p          →                =                  [                                                                      p                  1                                                                                                      p                  2                                                                                    ⋮                                                                                      p                  N                                                              ]                                    (                  Eq          .                                          ⁢          10                )                                                      x            →                    =                      [                                                            n                                                                                                  x                    a                                                                                                                    x                    b                                                                                                ⋮                                                                                                  x                    z                                                                        ]                          ⁢                                  ⁢        and                            (                  Eq          .                                          ⁢          11                )                                A        =                  [                                                                      10                  ⁢                                                            log                      10                                        ⁡                                          (                                              d                        1                                            )                                                                                                                    a                  1                                                                              b                  1                                                            ⋯                                                              z                  1                                                                                                      10                  ⁢                                                            log                      10                                        ⁡                                          (                                              d                        2                                            )                                                                                                                    a                  2                                                                              b                  2                                                            ⋯                                                              z                  2                                                                                    ⋮                                            ⋮                                            ⋮                                            ⋰                                            ⋮                                                                                      10                  ⁢                                                            log                      10                                        ⁡                                          (                                              d                        N                                            )                                                                                                                    a                  N                                                                              b                  N                                                            ⋯                                                              z                  N                                                              ]                                    (                  Eq          .                                          ⁢          12                )            
If the model is tuned against measurements, the vector {right arrow over (x)} is the unknown in Equation 9. As is well-known to those skilled in the art, the components of {right arrow over (x)} cannot be solved directly when there are more measured points in {right arrow over (p)} than unknowns in {right arrow over (x)} because it is an over-determined system of equations. However, by multiplying each side of Equation 9 by the transpose of A, AT, the system of equations can be solved:AT{right arrow over (p)}=ATA{right arrow over (x)}  (Eq. 13)Equation 13 represents a set of equations called the normal equations. Solving the normal equations for {right arrow over (x)} yields the set of parameters that minimizes the mean-squared error.
Despite these advances, path-loss models are still needed that are more accurate, that are more easily tuned, and that more easily lend themselves to computer automation than that depicted in Equation 13.